In my talk I consider a new approach to realizing the viable chaotic
inflation in supergravity, in four spacetime dimensions. Our approach
is based on the new version (or extension) of supergravity that we call
F(R) supergravity. The F(R) supergravity may be understood as the N=1
locally supersymmetric extension of f(R) gravity theories. In the first part
of my talk I briefly review our motivation (Bag Bang, inflation,
High-Energy Physics), and recall the basics of inflation. The
Starobinsky model of chaotic inflation is considered in detail, as an
example. Next, I outline a construction of F(R) supergravity in superspace,
and give some of its applications to the early Universe. In particular,
I explain how to embed the Starobinsky model into F(R) supergravity.
